A lottery is a form of legalized government gambling that involves the drawing of numbers for a prize. Lotteries are outlawed by some governments, while others endorse it to the extent of organizing a national or state lottery. It is common to find some degree of regulation of lottery by governments; the most common regulation is prohibition of sale to minors. Though lotteries were common in the United States and some other countries during the 19th century, by the beginning of the 20th century, most forms of gambling, including lotteries and sweepstakes, were illegal in the U.S. and most of Europe as well as many other countries. This remained so until well after World War II. In the 1960s casinos and lotteries began to re-appear throughout the world as a means for governments to raise revenue without raising taxes.
Lotteries come in many formats. For example, the prize can be a fixed amount of cash or goods. In this format there is risk to the organizer if insufficient tickets are sold. More commonly the prize fund will be a fixed percentage of the receipts. A popular form of this is the "50–50" draw where the organizers promise that the prize will be 50% of the revenue. Many recent lotteries allow purchasers to select the numbers on the lottery ticket, resulting in the possibility of multiple winners.
The purchase of lottery tickets cannot be accounted for by decision models based on expected value maximization. The reason is that lottery tickets cost more than the expected gain, as shown by lottery mathematics, so someone maximizing expected value should not buy lottery tickets. Yet, lottery purchases can be explained by decision models based on expected utility maximization, as the curvature of the utility function can be adjusted to capture risk-seeking behavior. More general models based on utility functions defined on things other than the lottery outcomes can also account for lottery purchase. In addition to the lottery prizes, the ticket may enable some purchasers to experience a thrill and to indulge in a fantasy of becoming wealthy. If the entertainment value (or other non-monetary value) obtained by playing is high enough for a given individual, then the purchase of a lottery ticket could represent a gain in overall utility. In such a case, the disutility of a monetary loss could be outweighed by the combined expected utility of monetary and non-monetary gain, thus making the purchase a rational decision for that individual.
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